45.12. Let n = 589. Note that n is the product of two primes. Most values in Z, have nine distinct cube roots. In this exercise we ask you to develop a way to factor n if, somehow, you were given all the cube roots of some a e Zn. Indeed, 201 is a perfect cube in Zm and here are all of its cube roots: 17, 54, 271, 301, 302, 358, 518, 549, and 575. Show how you can use these values to calculate the cube root of n. Note: We chose a small integer n to make your calculations feasible to perform with a calculator. Because n is so small, it might be easier just to use trial division. However, the point of this exercise is to show how it is possible to factor n quickly when given all nine cube roots of a perfect cube.

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Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.